An experimental study of near-cloaking G. Dupont 1,2,4 , O. Kimmoun 2,3,4 , B. Molin 2,3 , S. Guenneau 1,4 , S. Enoch 1,4 1 Institut Fresnel, UMR CNRS 7249, 13 397 Marseille cedex 20 2 IRPH ´ E, UMR CNRS 7342, 13 384 Marseille cedex 13 3 Ecole Centrale Marseille, 13 451 Marseille cedex 20 4 Aix-Marseille Universit´ e (AMU) In the past years there has been much research work on ”cloaking”, whereby some object is made ”invisible”. From electromagnetics the topic has been extended to other fields such as acoustics, structural mechanics and, more recently, hydrodynamics. In the water wave context, ”invisibility” means that the diffracted wave field is nil in the far-field at all azimuthal angles. This can usually be achieved only at one wave frequency. At the 26th IWWWFB Porter (2011) presented an application to the case of a vertical cylinder, rendered invisible by a local modification of the bathymetry in an otherwise constant depth ocean. This case was further investigated by Newman (2012). In this paper we report a similar study, where a vertical dihedral, at the end of the ECM wavetank, is at- tempted to be rendered invisible. Experimental set-up Our wave flume is about 15 m long and 65 cm wide. In the reported experiments the waterdepth was set at 40 cm. The beach at the end of the tank was removed and a rigid vertical plate was installed, from wall to wall, at an angle of 60 degrees, thereby achieving a dihedral. In this configuration a first series of regular wave tests was run, with wave number k mainly in the range π/b through 2 π/b (b being the tank width), meaning the reflected wave system, in the far-field, consists of two modes: the inline mode and the first sloshing (plus progressive) mode. The two components were separated by an array of 5 wave gauges over the width of the tank, set at different inline positions (the same experimental case being run as many times as different positions were used). In a second stage an ”invisibility carpet”, consisting in 18 vertical poles, with trapezoidal cross-sections, was set in front of the dihedral. The same regular wave tests were run, and the reflected inline and sloshing modes were separated from the wave gauge measurements. Successful ”invisibility” implies that the sloshing modes vanish and only the inline reflected mode remains. Numerical determination of the reflected wave system The problem was formulated within the frame of linearized potential flow theory, and solved numerically with the COMSOL Multiphysics software. In the dihedral alone case (without the ”invisibility carpet”) a semi-analytical method, described below, was also used to validate COMSOL’s results. Due to the wall-sided geometry the linearized velocity potential writes Φ(x,y,z,t)= ℜ  −i A I g ω cosh k(z + h) cosh kh ϕ(x, y)e -i ωt  (1) where A I is the amplitude of the incoming waves, h the waterdepth, ω the frequency and k the wave number. The reduced potential ϕ satisfies the Helmholtz equation Δϕ + k 2 ϕ = 0 in the fluid domain, no-flow conditions at the solid walls and appropriate ingoing and outgoing conditions at x →∞. Dihedral alone Figure 1 shows the geometry at the end of the tank. It consists in two overlapping rectangular sub-domains: – the angular sector 0 ≤ R ≤ 2 d ;0 ≤ θ ≤ π/3 (inside the green contour in figure 1). – the semi-infinite strip d ≤ x< ∞ ;0 ≤ y ≤ b with d = b √ 3/3 (inside the red contour). Within the first sub-domain the reduced potential ϕ takes the general form: ϕ 1 (R, θ)= ∞  m=0 A m J 3m (kR) J 3m (2kd) cos 3mθ (2) with J 3m the Bessel function of the first kind. Within the second sub-domain it can be written as: ϕ 2 (x, y)=e -i kx + ∞  n=0 B n cos λ n y e -αn (x-d) (3)